Angular velocity is the rate at which an angular displacement changes with respect to time. It measures the speed at which an object revolves around a fixed axis or point.

Unlike linear velocity(angular velocity calculator using linear velocity)which measures the speed of an object in a straight line, angular velocity measures the rotational speed of an object in circular motion. It quantifies how quickly an object's angular position changes over time.

To understand the concept, consider a spinning wheel. As the wheel rotates, each point on its circumference moves through an angular displacement. Angular velocity describes how rapidly these points move relative to the center of the wheel.

Formula of Angular Velocity :
ω = Δθ / Δt
Where :
  • ω (omega) denotes angular velocity
  • Δθ indicates the angle that the rotating object changed all through the time interval Δt
  • Δt represents the change in time

Units of Angular Velocity :

1. Radians per Second (rad/s) :
  • The angle subtended by an arc whose length is equal to the circle's radius is measured in radians, which are units of angular measurement.
  • Radians per second (rad/s) denote the angular velocity expressed in terms of the number of radians an object rotates through in one second.
2. Degrees per Second (°/s) :
  • Another widely used angular measurement unit, particularly in everyday contexts, is degrees.
  • Degrees per second refers the angular velocity in terms of the number of degrees an object rotates through in one second.
3. Revolutions per Minute (RPM):
  • The number of complete revolutions an object makes in a minute is represented as the RPM.
  • For measuring rotational speed, it is a convenient unit, particularly in situations where revolutions make more sense than radians or degrees.
  • The following conversions must be made in order to convert radians per second (rad/s) or degrees per second (°/s) to revolutions per minute (RPM):
    • 1 radian per second (rad/s) ≈ 9.5493 revolutions per minute (RPM)
    • 1 degree per second (°/s) ≈ 0.16667 revolutions per minute (RPM)

How Angular Velocity Calculator Using Angle and Time Works: A Step-by-Step Example

Question :

Calculate the angular velocity in radians per second of a wheel that rotates through an angle of 2.5 radians in 4 seconds.

Answer:
Given:
  • Angle of rotation, Δθ = 2.5 radians
  • Time taken,Δt = 4 seconds
To find the angular velocity (ω), we will use the formula:
ω = Δθ / Δt
ω = 2.5 radians / 4seconds
ω = 0.625 radians per second
Therefore, the angular velocity of the wheel is 0.625 radians per second.

Why to use our Angular Velocity Calculator?

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